Truth table size for a 4-input NAND gate How many rows (input combinations) are required in the truth table of a four-input NAND gate?

Introduction / Context:
Truth tables enumerate every possible input combination for a logic function. Knowing how many rows are required allows designers to plan verification efforts and to reason about complexity in combinational logic design.

Given Data / Assumptions:

• Gate type: NAND.
• Number of inputs: 4 (A, B, C, D).
• Binary logic levels (each input is 0 or 1).

Concept / Approach:

The count of input combinations for an n-input logic function equals 2^n. This is independent of the gate type (AND, OR, NAND, NOR, etc.) because it depends only on the number of inputs and the binary nature of each input variable.

Step-by-Step Solution:

Verification / Alternative check:

List the inputs in binary counting order from 0000 to 1111; you will enumerate exactly 16 unique rows. Regardless of the gate's function, this exhaustive list is the complete set of input possibilities for four binary variables.

Why Other Options Are Wrong:

• 2 and 4 correspond to 1- or 2-input functions, not 4 inputs.
• 8 corresponds to 2^3, the count for 3 inputs.
• 32 corresponds to 2^5, the count for 5 inputs.

Common Pitfalls:

• Confusing the number of truth table rows with the number of gates used.
• Thinking gate type affects row count; it does not.

Final Answer:

16